Growth And Development

Sample Solution

e used with replacement while obtaining same results because the probability of drawing the same person is very small. Advantages of this type are that is free of classification error, it requires minimum advance knowledge of the population other than the frame and it allows one to draw externally valid conclusions about the entire population. Nevertheless, the survey conductor should be careful to make an unbiased random selection of individuals so that if a large number of samples were drawn, the average sample would accurately represent the population. Generally, it is appropriate to use this method because its simplicity makes it relatively easy to interpret data collected in this manner and it best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity. As a consequence, if these conditions do not hold, then other methods may be a better choice, [see 5, “Simple Random Sample”, para. 6]

3.2 Systematic Sampling

Like simple random sampling, systematic sampling gives each element in the population the same chance of being selected for the sample. It differs, however, from simple random sampling in that the probabilities of different sets of elements being included in the sample are not all equal (Kalton 1983)[see 3]. For this method, the sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k (the sampling interval). This is calculated as k=N/n, where n is the sample size and N is the population size, [see 6, “Systematic Sampling”, para. 1]. For example, assume that a teacher wants to sample 200 students from a school with 2000 students. The sampling fraction is 2000/200=10, so every 10th student is chosen after a random starting point between 1 and 10. If the random starting point is 3, then the students selected are 3,13,23,33,43,53,…,1993. As an aside, if every 10th student is a foreigner then this pattern could destroy the randomness of the population. However, there are situations where the sampling fraction contains decimal places (e.g. 2150/200=10.75). In these situations, the random starting point should be selected as a noninteger between 0 and 10.75 to ensure that every student has an equal chance of being selected. Furthermore, each noninteger selected should be expressed as the previous integer number. For instance, in our example, if the random starting point is 3.6, then 10.75 repeatedly to 3.6 gives 14.35, 25.1, 35.85 and so on. The subsequent selections are the fourteenth, twenty-fifth, thirty-fifth, etc., students. The interval between selected students is sometimes 10 and sometimes 11. In general, systematic sampling is appropriate to be applied only if the given population is logically homogeneous becau